Coarse embeddings into c₀(Γ)

2017/03/06 by Hajek, Petr, Schlumprecht, Thomas
#54D20 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 46B26 #Secondary 54E15

paper · doi:10.48550/arxiv.1703.01891

Abstract

Let λ be a large enough cardinal number (assuming GCH it suffices to let λ=ℵ_ω). If X is a Banach space with dens(X)≥λ, which admits a coarse (or uniform) embedding into any c₀(Γ), then X fails to have nontrivial cotype, i.e. X contains ℓ_∞ⁿ C-uniformly for every C>1. In the special case when X has a symmetric basis, we may even conclude that it is linearly isomorphic with c₀(densX).

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